When a disturbance (for example, lightning strike) occurs on an overhead high-voltage transmission line, high magnitudes of current flow through the line conductor and connected equipment to the point of the disturbance. The heavy current can quickly damage the line conductor and connected equipment (for example, transformer bank).
Modern protective relays are available that detect the presence of a disturbance on overhead transmission lines and send commands to open the circuit breakers at each end before any damage occurs. However, the systems currently in use have a number of significant drawbacks.
Referring to FIG. 1, the situation is illustrated where a lightning strike hits the upper line conductor between transmission towers #1 and #2. The voltage at the strike builds rapidly until it flashes over to ground and high magnitude current flows. If the distance to the fault is known, line crews can be quickly dispatched for any necessary repair. Otherwise a lot of time and expense is required to patrol the overhead line for possible damage.
Modern protective relays at terminal S (to the left of FIG. 1) and terminal R (to the right of FIG. 1) both monitor the overhead transmission line by measuring the local voltage and current flow at their respective locations. During a fault, voltage drops and current increases.
Under a conventional method of the prior art known as the “single-ended method”, the relays calculate the distance to the fault using data (voltage and current) measured at the respective locations. The single-ended method has significant error when there is fault resistance (for example, wind blows tree into line conductor) and power is flowing through the line. Also, zero-sequence mutual coupling with other overhead transmission lines is a significant source of error for existing single-ended methods.
Thus, distance-to-fault locating technology that has been used for years in commercial applications requires data only from one end of the overhead transmission line to calculate the distance to the fault. FIG. 2 illustrates such an application wherein the voltage and current measured at the two ends of a faulted overhead transmission line during a single phase-to-line fault. “m” is the per-unit distance to the fault with respect to terminal S. Therefore,    m•ZL=total impedance of the phase to the point of the fault from terminal S    (1−m)•ZL=total impedance of the phase to the point of the fault from terminal R    RF=Total fault resistance    VS=Faulted phase voltage measured at terminal S    IS=Faulted phase current measured at terminal S    VR=Faulted phase voltage measured at terminal R    IR=Faulted phase current measured at terminal R
A simple explanation of the most popular single-ended method used today is that the local fault voltage is divided by the local fault current to determine the faulted phase loop impedance, ZLOOP. The imaginary part of ZLOOP (XF) is then calculated to ignore any fault resistance, which can be significant.ZLOOP=VS/IS  (1.1) XF=Im[ZLOOP]  (1.2)                 Where Im[•] denotes the imaginary part of the argument.        
The fault reactance (XF) is then divided by the total reactance of the overhead transmission line to estimate the per-unit distance to the fault with respect to terminal S.m=XF/XL  (1.3) 
The main problem with the single-ended method is the assumption that the faulted phase current from both ends of the overhead transmission line are in-phase. If there is load flow, this is typically not the case. As the angular difference between IS and IR increases, so does the error.
The error occurs because the faulted phase voltage measured at terminal S (VS) is dependent on the faulted phase current flowing from terminal R (IR).VS=IS•m•ZL+(IS+IR)•RF  (1.4) 
If there is an angular displacement between IS and IR, a reactance component is introduced due to the voltage drop across the fault resistance (see FIG. 3) when the imaginary part of the faulted phase loop impedance is calculated.                                           V            S                    /                      I            S                          =                              m            ·                          Z              L                                +                                                                      I                  S                                +                                  I                  R                                                            I                S                                      ·                          R              F                                                          (        1.4        )             VS/IS=m•ZL+(1+α)•RF  (1.5)Where α=IR/IS  (1.6) 
If the angle of IS is equal to the angle of IR, the imaginary part of α•RF is equal to zero; otherwise the value is non-zero and significant error is introduced.
This problem for the single-ended method has always been in existence since the method was first introduced because fault resistance is typically present during a fault.
As mentioned above, another common problem with the single-ended method is zero-sequence mutual coupling. When two or more overhead transmission lines share the same right-of-way, there is coupling between the lines in the zero-sequence network since these components are in-phase.
FIG. 4 illustrates a single phase-to-ground fault on Line #1. There is zero-sequence mutual coupling between the two overhead transmission lines because they share the same right-of-way. Therefore, the faulted phase current flowing in Line #2 (IS2) affects the faulted phase voltage measured on Line #1 at terminal S.
If IS1 and IS2 flow in opposite directions, the faulted phase voltage measured on Line #1 at terminal S decreases; therefore, the faulted phase loop impedance measured at terminal S for Line #1 is reduced (ZLOOP=V−/I) and the distance-to-fault calculation is closer to terminal S than the actual location of the fault.
If IS1 and IS2 flow in the same direction, the faulted phase voltage measured on Line #1 at terminal S increases; therefore, the faulted phase loop impedance measured at terminal S for Line #1 is increased (ZLOOP=V+/I) and the distance-to-fault calculation is further from terminal S than the actual location of the fault.
The problems associated with zero-sequence mutual coupling exist because of the following:                The modern protective relay calculating the distance-to-fault does not account for the faulted phase current flowing in the parallel overhead transmission line.        The calculation is not immune to zero-sequence quantities.        
This problem for the single-ended method has always been in existence since the method was first introduced because there are many overhead transmission lines that share right-of-way with others.
One attempt to solve the problem of zero-sequence mutual coupling with a parallel overhead transmission line is to measure the faulted phase current flowing in the parallel line. This extra measurement allows the distance-to-fault calculation to account for the voltage drop/rise on the faulted phase of the monitored line due to zero-sequence mutual coupling and account for its effect.
Unfortunately, when the parallel overhead transmission line is out-of-service and grounded at both terminals (see FIG. 5), loop current flows in the grounded line for faults involving ground on the parallel in-service line. The loop current cannot be measured since the current transformers are outside of the loop flow. Therefore, the distance-to-fault calculation on the parallel in-service line is too close at one terminal, and too far at the other.
Double-ended distance-to-fault locating systems that use non-synchronized quantities have been proposed by the process of U.S. Pat. No. 4,107,778 (Nii, et al.), U.S. Pat. No. 5,455,776 (Novosel), and U.S. Pat. No. 6,256,592 (Roberts, et al.). All three of these methods are complex to implement primarily because the voltage and current measurements are not time-synchronized.